Network analyzers are instruments that characterize networks. The characterization result is based on conventions and define how the network will perform under various conditions. In signal integrity applications, the common network parameters in use are scattering parameters, or s-parameters. S-parameters define port to port relationships in a network when the network is driven by a source whose impedance is set to the reference impedance and all other ports are terminated in that same reference impedance. This convention allows scattering parameters to completely define the behavior of a network under any other driving and termination conditions.
The standard instrument for s-parameter measurement is the vector network analyzer (VNA). This instrument stimulates a network with sinusoidal incident waveforms and measures the reflected sinusoidal waveforms at the network ports. This instrument is most commonly used in the field of microwave analysis.
Another instrument used for s-parameter measurement uses techniques called time domain reflectometry (TDR) and time domain transmission (TDT) (the commonly used acronym TDR will be used to represent both techniques, the name of the instrument itself, and time domain analysis in general). TDR stimulates a network with an incident step, or a step-like waveform and measures reflected waveforms at the network ports. This instrument is most commonly used in the field of signal integrity.
FIG. 1 shows a d-port (d≧1) network including a device under test (DUT) [1], “psk” [2], indicates k-th pulser-sampler. The device under test (DUT) [1] has unknown s-parameters and it is desired to measure and determine these s-parameters in order to characterize the device. Each pulser-sampler device has a pulser that is capable of sending a stimulus signal and a sampler that measures the signal reflected from DUT [1]. S-parameters of the DUT [1] define the port to port transfer function of the DUT. For example,
                                          S            kk                    =                                    b              k                                      a              k                                      ,                            (        1        )            is the transfer function for port k that characterizes the reflection coefficient of port k. Here ak is the frequency domain representation of the input signal to port k of the DUT and bk is the frequency domain representation of the signal reflected from port k of the DUT. All the other ports of the DUT are terminated so that no signal reflects from those ports. Similarly,
                                          S            jk                    =                                    b              j                                      a              k                                      ,                            (        2        )            defines the transmission coefficient between ports k and j. Here ak is the frequency domain representation of the input signal to port k of the DUT and bj is the frequency domain representation of the signal that gets transmitted from port k of the DUT to port j of the DUT. All the other ports of the DUT are terminated so that no signal reflects from those ports. Also, under ideal conditions, the sampler is such that it does not reflect any incoming signal. To measure the s-parameters of the d port DUT [1], reflected waves received at, and returned via, the d ports of the device would be measured under d independent measurement conditions. The equations that relate, for each measurement condition mε{1, . . . , d}, the reflected waves to the incident waves are shown in Equation 3, below:
                                          [                                                                                s                    11                                                                                        s                    12                                                                    …                                                                      s                                          1                      ⁢                      d                                                                                                                                        s                    21                                                                                        s                    22                                                                    …                                                                      s                                          2                      ⁢                      d                                                                                                                    …                                                  …                                                  …                                                  …                                                                                                  s                                          d                      ⁢                                                                                          ⁢                      1                                                                                                            s                                          d                      ⁢                                                                                          ⁢                      2                                                                                        …                                                                      s                                          d                      ⁢                                                                                          ⁢                      d                                                                                            ]                    ·                      [                                                                                a                                          1                      ⁢                      m                                                                                                                                        a                                          2                      ⁢                      m                                                                                                                    …                                                                                                  a                                          d                      ⁢                                                                                          ⁢                      m                                                                                            ]                          =                  [                                                                      b                                      1                    ⁢                    m                                                                                                                        b                                      2                    ⁢                    m                                                                                                      …                                                                                      b                                      d                    ⁢                                                                                  ⁢                    m                                                                                ]                                    (        3        )            where, for iε{1, . . . , d}, aim is a complex number corresponding to amplitude and phase of the incident wave at port i under measurement condition m, and where bim is a complex number corresponding to amplitude and phase of the reflected wave at port i under measurement condition m. Ideally, one would apply stimuli to each of the d ports under d unique measurement conditions (i.e., define the incident waves aim) and then measure the reflected waves at each of the d ports under these d measurement conditions (i.e., measure bim) in order to determine the unknown s-parameters. If the matrices A−(aim) and B−(bim) are defined, then the matrix S−(sim) of unknown s-parameters is S−B·A−1.
Note that the pulser-sampler device shown in FIG. 1 may be a combination of the pulser and the sampler or it may be two separate devices. For convenience, in all the subsequent figures, they are represented as one device and are meant to imply one pulser and one sampler. Also, a pulser may comprise a TDR step like source or an impulse like source or may correspond to a VNA source or that of any VNA-like instrument's signal source. The purpose of such a pulser is to excite the DUT port with a stimulus signal with desired frequencies. Similarly a sampler may comprise of a TDR sampler capable of measuring a step like waveform or an impulse like waveform, or a VNA like receiver. The purpose of such a sampler is to measure the signal coming from the DUT ports. For the purpose of this application a device capable of sending such a signal is referred to as a pulser and a device capable of measuring the incoming signal will be referred to as a sampler.
In practice, the pulsers and samplers are non-ideal. One needs cables and connectors to connect the DUT to these pulsers and samplers. The cables and connectors can be lossy. There can be a mismatch in impedance of cables and connectors. These non-idealities result in systematic errors in the measurements of s-parameters. In order to eliminate such errors, the measuring device needs to be calibrated. A process of calibration involves first assuming a model for such systematic errors. Such a model is referred to as an error term model. The coefficients of this model are calculated using a calibration procedure. Calibration procedure involves connecting a device with known characteristics (known s-parameters for example) instead of a DUT. Such a device is referred to as a calibration standard. An input signal is applied and the reflections due to this known device is measured. Multiple such known calibrations standards are connected and responses measured. All these measurements and the known characteristics of the calibration standards are used to generate the coefficients of the error term model (“Error terms from calibration [3]” in FIG. 2). Currently there are different calibration techniques in the literature, for example Short-Open-Load-Thru (SOLT) calibration, Thru-Reflect-Line (TRL) calibration etc. The most commonly used calibration method is the SOLT method that uses known short, open, load and thru calibration standards. The most commonly used error term model is the 12-term error model described in “Agilent AN 1287-3 Applying Error Correction to Network Analyzer Measurements—Application Note”. For each of these calibration techniques the reference plane is defined as the interface where these calibration standards are connected. All the subsequent s-parameter measurements made at this plane are referred to as raw s-parameters. Calibrated s-parameters are then calculated from these raw s-parameters and the error term model by using the algorithm described in “A General, Closed Form Solution to Multi-port S-Parameter Calculations 72nd ARFTG Microwave Measurement Conference December 2008”.
There are a number of drawbacks in measuring s-parameters utilizing prior art procedures:                The calibration is performed manually by connecting the calibration standards at the end of the measuring instrument. Besides being a time consuming exercise prone to operator errors, it also results in the mechanical wear and tear of the calibration standards.        The number of pulser-sampler blocks increases with the number of DUT ports, thereby increasing the cost of providing a device to perform such measurements. To circumvent the problem, there have been proposed methods that use a switch matrix that connects a two port VNA or VNA-like instrument to an N-port DUT. For example U.S. Pat. No. 5,578,932 by Vahe Adamian provides one such description.        Currently there are automatic calibration instruments available. U.S. Pat. No. 5,587,934 by Oldfield et al. provides one such description. But even these instruments suffer from the limitation of manually connecting them to the measuring device for calibration and disconnecting them to connect the DUT to the measuring instrument.        
What is needed is a measuring instrument that can calibrate itself without requiring an operator to connect different calibration standards. What is also needed is a measuring instrument whose cost remains within reasonable bounds with the increase in number of ports in the network.